MonadLayerControl

MonadLayerControl is possible to use to access lower monad layers in invariant position, as in so-called "control operations".

Three external laws:

def layerMapRespectsLayerControl[A](m: M[A], f: Inner ~> Inner) = {
  layerMapK(m)(f) <-> layerControl(run => f(run(m)).flatMap(restore)
}

def distributionLaw[A](nt: State ~> State, st: State[A]) = {
  restore(nt(st)) <-> layerControl[State[A]](_ (restore(st)).map(nt(_))).flatMap(restore)
}

def layerControlIdentity[A](ma: M[A]) = {
  ma <->
    layerControl[Inner[State[A]]] { cps =>
      cps(ma).pure[Inner]
    }.flatMap(layer).flatMap(restore)
}